Before I list the replies, here is some background. The Higgs mechanism describes an invisible field that, it is argued, split one
force into two soon after the birth of the universe. Specifically, it
divided an ancient "electroweak" force into the electromagnetic and
weak forces we see at work today. The latter is seen in some
radioactive decay processes, and is involved in creating sunshine.

The Higgs field splits the electroweak force by giving mass to the
particles that carry the weak force (the W & Z bosons) and leaving the
particle that carries the electromagnetic force (the photon) massless.
The Higgs boson is the quantum particle associated with the Higgs
field.

What I'm wondering is... can anyone hazard a guess as to the possibility at some point in the future of humans being able to manipulate the Higgs mechanism so as to give photons some kind of mass? I'm thinking they obviously couldn't go at the speed of light anymore, so could we make 'slow light'?

(this only partially 'answers' the title of the question) adding mass to photon destroys local gauge invariance -> charge is no longer conserved
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pcrDec 7 '11 at 2:21

@pcr: indeed, the destruction of local gauge invariance was the main complaint with the BCS theory. This complaint is specious, as explained by the Higgs mechanism (or the earlier Landau model), but it still kept some people from fully accepting BCS until the late 1960s. When you have a charged condensate, the condensate dynamics are responsible for taking charge into and out of a localized system, and different charges are no longer in different superselection sectors.
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Ron MaimonDec 24 '11 at 13:18

3 Answers
3

We already can do this in materials--- it is called "superconductivity". The phenomenon for photons was understood before the phenomenon in the weak interactions, and the description of superconductivity by Landau, and the Bardeen Cooper Schriefer model for fermionic paired condensates, was the inspiration for Nambu's fermion vacuum condensate idea, and Brout and Englert's later point-particle superconducting Higgs mechanism.

Photons do not go slower in a superconductor, they do not go at all. Superconductors don't have photon excitations at all, and if you have an electric and magnetic field in the superconductor trying to propagate, the fields away exponentially.

It is certain that we won't be able to do this in vacuum, because we know all the fields around us are stable. In order to make an instability in the field, we have to alter the fundamental constants in such a way that a charged field makes a superconducting condensate. In order to alter the constants, we would need a certain energy density per unit volume which is going to be practically infinite for the purposes of engineering.

But the condensed matter analog, the superconductor, is a perfect analog, and we understand the dynamics of what would happen in this situation simply by examining what happens in a superconductor, and extrapolating to the situation where the material doesn't break Einstein's relativity invariance with respect to constant motion.

Ginzburg–Landau theory gives an impression of Lorentz/Poincaré invariance (although Ī didn’t investigate whether does it obey the “true” c), but one should understand that superconductors, fundamentally, are not Lorentz-invariant in any sense.
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Incnis MrsiOct 29 '14 at 11:13

@IncnisMrsi: yes, that's the one difference--- material superconductivity picks out a rest frame, while relativistic condensates don't. But other than being relativistically invariant, they are just the same as nonrelativistic condensates.
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Ron MaimonOct 29 '14 at 23:13

It would be a neat idea, but as far as current (or foreseeable future) physics is concerned, it's pretty much flat-out impossible.

Basically, the Higgs mechanism works on a very fundamental level. If we are ever to be able to manipulate it, it will have to turn out that the Higgs mechanism (and the standard model as a whole) is not a fundamental theory, but just a consequence of some even more fundamental theory, which we will then have to discover and understand. The thing is, in general, "more fundamental" theories tend to involve processes that happen at progressively higher and higher energies, which makes them very hard to even observe, much less control. If you think about it, we needed a major international collaboration (the LHC) to simply see any nontrivial consequence of the Higgs mechanism. How much more complicated and expensive would it be to get access to whatever theory may underlie the standard model? I doubt that is something we can expect to see any time soon.

+1 Thanks. I'm a babe in the woods of particle-physics. It would be nice to get some more understanding of how the Higgs field gives mass to things.
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Mike DunlaveyDec 7 '11 at 1:46

OK, then, I will add some math to this later on. (Actually, on second thought, you could ask that as a separate question. Surprisingly enough, it seems like nobody has yet asked something along the lines of "How does the Higgs mechanism work?" and I think that would be a good question to have on the site.)
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David Z♦Dec 7 '11 at 1:53

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@David: I don't think I understand your comment that photons in a material are massive. Can you explain? The photons still have a gapless dispersion - they go slower than the speed of light, sure, but thats not really a "massive" photon. Thats just a consequence of the breaking of Lorentz symmetry. As Ron says, the correct condensed matter analog of a massive photon is superconductivity.
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BebopButUnsteadyDec 23 '11 at 16:08

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@David: -1, please fix the massive photon business BebobButUnsteady points out. Mass is an energy gap, not a different dispersion slope. Photons don't get mass in non-superconducting materials precisely because of gauge invariance. They can't get massive, they can only slow down or speed up (and they can't speed up for too many wavelengths, so that they stay causal). In order to get a mass you need a charged condensate to break the symmetry that the photon gauges.
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Ron MaimonDec 23 '11 at 19:55

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@IncnisMrsi: I was complaining that he claims that photon propagation in a medium, where the speed of light is reduced, is an example of making light massive. The definition of "massive" is quadratic dispersion with a gap, not linear dispersion with an altered propagation speed.
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Ron MaimonOct 29 '14 at 23:16